Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras

TL;DR

This paper classifies irreducible Harish-Chandra modules over map full toroidal Lie algebras, showing they are either cuspidal or highest weight modules and are single point evaluation modules.

Contribution

It provides a complete classification of these modules, revealing their structure as either cuspidal or highest weight and as single point evaluation modules.

Findings

Modules are either cuspidal or highest weight.

All modules are single point evaluation modules.

Classification extends understanding of toroidal Lie algebra representations.

Abstract

A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is either a cuspidal or a highest weight module. Furthermore, we prove that they turn out to be single point evaluation modules.